Gravity gradiometer

ABSTRACT

A gravity gradiometer for measuring off-diagonal components of the gravitational gradient tensor includes a housing comprising a pair of electromagnetic shield enclosures (22, 23) arranged one inside the other, and a body (25) including superconducting material mounted within the inner enclosure (23) for fine pivotal flexure about an axis passing substantially through the center of mass of the aforesaid body. An array of superconducting coils (30) is supported by the outer enclosure (22) and positioned in close proximity to the aforesaid body (25) for diamagnetically applying a rotational force to the body with respect to the axis of flexure and/or for responding by modulation of inductance to pivotal flexure of the body arising from a gravitational gradient across the body. The array is arranged to apply the rotational force in both rotational directions and to respond to flexure in either rotational direction. Also disclosed is a flexural pivot bearing which comprises a pair of members (28, 31) with opposed close-spaced faces. These faces are joined by a web (29), of microscopic thickness, in a plane intersecting the faces. The members and the web are consisted of an integral body of substantially uniform, material, and the members are adapted for pivoted mutual flexure about a pivot axis aligned along said web.

This is a continuation of application Ser. No. 08/367,757 filed Jan. 3,1995 now U.S. Pat. No. 5,668,315, which in turn is a continuation ofapplication Ser. No. 08/115,677 filed Sep. 2, 1993, now abandoned, whichin turn is a continuation of application Ser. No. 07/688,528, filed asPCT/AU89/00543, Dec. 20, 1989, now abandoned.

FIELD OF THE INVENTION

This invention relates to a gravity gradiometer, especially agradiometer for measuring off-diagonal components of the gravitationalgradient tensor, and also provides a novel flexural pivot bearing whichhas particular, though certainly not exclusive, application to gravitygradiometry.

The gravimeter is widely employed in geological surveying to measure thefirst derivatives of the earth's gravitational potential function--thegravity field. Because of the difficulty in distinguishing spatialvariations of gravity from temporal fluctuations of the accelerations ofa moving vehicle, these measurements can be made to sufficient precisionfor useful exploration only with land-based stationary instruments. Thisdifficulty is in principle avoided by measurement of the secondderivatives of the potential--gravity gradients--but only limitedsuccess has been met to date in developing a satisfactory gradiometerinstrument. Gravity gradiometry is thought especially appropriate to thelocation of geological structures bearing hydrocarbons, to geologicalmapping, and to locating high density (e.g., sulphides and iron ore) andlow density (e.g., potash) mineral deposits.

Although it is not strictly correct to talk about the gradient ofgravity, usage of the term has been universally adopted and will be usedherein also. More formally, the second derivatives of the gravitationalpotential are termed gradients of gravity and constitute the gravitygradient tensor with components g_(xx), g_(xy) . . . g_(zz), adoptingthe convention of taking the Z-axis parallel to the local vertical.There are nine such components, only five of which are independent sincethe tensor is apparently symmetric and the potential is a scalar fieldobeying Laplace's equation.

BACKGROUND ART

The key elements of a gravity gradiometer are a pair of substantiallyidentical spaced masses and the object is to measure differences betweenthe gravitational force on the respective masses. Effectiveness requiresmeasurements of this difference when it approaches only one part in 10¹²of normal gravity. Approaches to measuring gravity gradients have thusfar fallen into two broad classes. The first of these entailsdifferential modulation of a signal or parameter by the differencebetween the gravitationally induced accelerations of the two masses. Thesecond technique involves direct measurement of the net gravitationalacceleration of one mass relative to the other.

British patent publication 2022243 by Standard Oil Company discloses agravity gradiometer in the first class. An element, described in thepatent publication as a mass dipole, is mounted coaxially on one end ofa photoelastic modulator element positioned in the cavity of a ringlaser tube to differentially modulate circular polarization modes inresponse to application of a torque. In a preferred form, two massdipoles as described are mounted on opposite ends of the modulatorelement to balance rotational acceleration noise. A closely relateddevelopment by the same inventor, Lautzenhiser, described in U.S. Pat.No. 4,255,969, employs actual mass dipoles in conjunction withrespective photoelastic modulator elements.

Another modulation technique involves rotating a platform which issupporting suitable arrangements of mass pairs. Various instruments ofthis kind are summarised by Jekeli at 69 EOS (No. 8). One of these, byMetzger, has been further developed and consists of electronicallymatched pairs of accelerometers on a rotating platform. The platformmodulates the sum of opposing acceleration signals with a frequencytwice its rotational frequency. These modulation systems call forextremely exacting uniformity in the rotation and require the use ofbearing, rotational drive and monitoring technology which is not yet ofa standard to render the instruments practicably suitable on anappropriate scale for airborne or moving land-based measurements forgeophysical resource exploration, as opposed to geodetic surveying. Thealternative of directly measuring gravity gradient componentsnecessitates a very high degree of electronic, magnetic, thermal andvibration isolation to achieve the measurement accuracy needed. Machinesthus far have had poor spatial resolution and a high noise level.

An instrument for measuring the diagonal components g_(xx), g_(yy) andg_(zz) of the gravitational gradient tensor is described by van Kann etal in the publication IEEE Trans. Magn. MAG-21, 610 (1985) and furtherelaborated in the NERDDP End-Of-Grant Report (1986) on project no. 738.This instrument consists of a pair of accelerometers mounted with theirsensitive axes in line. The difference in displacement of theaccelerometers is proportional to the component of the given tensorgradient and is sensed by the modulated inductance of a proximatesuperconducting coil. This instrument suffers from the disadvantage thatdiaphragm springs serve both as mounts for the masses and as gradientsensors. The former of these roles calls for a greater stiffness in thesprings while the sensing role necessitates enhancement of the springs'softness. It is also very difficult with the van Kann instrument toachieve axial alignment of the masses and trimming of the springmountings with the accuracy needed to obtain the common mode.acceleration rejection ratios necessary for the accuracy sought.

SUMMARY OF THE INVENTION

It has been realised, in accordance with a first aspect of theinvention, that significant advantages can be obtained relative to thevan Kann instrument, and direct measurement of gravitational gradientsmade more easily achievable, by instead measuring off-diagonalcomponents of the gravitational gradient tensor by means of one andpreferably two pivoted bodies supported by a flexural pivot, and bymaking the provision of mass support by the relatively stiff tensilespring property distinct from the sensing function provided by therelatively soft bending spring property.

The invention accordingly provides, in its first aspect, a gravitygradiometer for measuring off-diagonal components of the gravitationalgradient tensor, which includes a housing comprising a pair ofelectromagnetic shield enclosures arranged one inside the other, and abody including superconducting material mounted within the innerenclosure for fine pivotal flexure about an axis passing substantiallythrough the centre of mass of the aforesaid body. An array ofsuperconducting coils is supported by the outer enclosure and positionedin close proximity to the aforesaid body for diamagnetically applying arotational force to the body with respect to the axis of flexure and/orfor responding by modulation of inductance to pivotal flexure of thebody arising from a gravitational gradient across the body. The array isarranged to apply the rotational force in both rotational directions andto respond to flexure in either rotational direction.

The two enclosures are conveniently close fitting oblong boxes and thepivotally mounted body is preferably a matching solid body of acomplementary shape. In a preferred embodiment, there is asuperconducting coil on opposite sides of each arm of the quadrupolebody to either side of the flexure pivot axis. There may also be furthercoils to either side of the body at the axis and at each end of thebody, for monitoring translational movement of the body.

The term "superconducting" is used herein, according to the normalconvention, to denote a material which at least is superconducting belowa characteristic critical temperature. A suitable such material isniobium, which has a critical temperature of about 9K.

The aforedescribed gravity gradiometer is of course preferably supportedin a system which is shielded electrically, magnetically, thermally andvibrationally in a manner similar to that described in theaforementioned End-Of-Grant Report.

There are preferably a pair of gradiometers coupled together in a singleinstrument with the axes of flexure of their respective bodies paralleland preferably coincident, but with the bodies aligned mutuallyorthogonally and orthogonal to the axes of flexure.

The pivotal flexural mounting for the mass quadrupole body may comprisea flexure bearing such as the commercially available Bendix pivot. Ithas been found, however, that: this bearing is less than whollysatisfactory as it is constructed of several different metals securedtogether and this creates significant problems due to different thermalexpansion coefficients and other parameter variations which becomecritical at the kind of accuracy desired in thus present context.

The invention therefore provides, in a second aspect, a flexural pivotbearing which comprises a pair of members with opposed close-spacedfaces. These faces are joined by a web, of microscopic thickness, in aplane intersecting the faces. The members and the web are comprised ofan integral body of substantially uniform material, and the members areadapted for pivoted mutual flexure about a pivot axis aligned along saidweb.

A particularly useful application of the invention in its second aspectis as the mounting for the mass quadrupole body of the aforedescribedgravity gradiometer according to the first aspect of the invention. Forthis purpose the bearing is preferably cut from a single mass of asuperconducting material such as niobium.

The two members of the bearing may be a generally annular body and asecond body within the annular body.

In a more general third aspect, the invention provides a gravitygradiometer having broad application and not requiring vigoroussensitivity needing superconducting componentry comprising:

a housing;

a body mounted within the housing for fine pivotal flexure about an axispassing substantially through the centre of mass of said body; and

an array of transducer devices supported within said housing andpositioned in close proximity to said body for applying a rotationalforce to said body with respect to said axis of flexure and/or forresponding by modulation of inductance or capacitance to pivotal flexureof the body arising from a gravitational gradient across said body,wherein the array is arranged to apply said force in both rotationaldirections and to respond to flexure in either rotational direction.Preferably, in this case, said body is mounted by means of a flexuralpivot bearing comprising a pair of members with opposed close-spacedfaces, which feces are joined by a web, of microscopic thickness, in aplane intersecting the faces, wherein said members and said web arecomprised of an integral body of substantially uniform material, andsaid axis of flexure is aligned along said web.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in greater detail, by way of exampleonly, with reference to the accompanying drawings in which:

FIG. 1 is a diagrammatic axial cross-section of a gravity gradiometerassembly according to the first aspect of the invention supported on agimballed mounting within a vacuum can for rotationally stabilisedcryogenic operation:,

FIG. 2 is an enlargement of part of FIG. 1, showing the gradiometerassembly at actual size;

FIG. 3 is a cross-section on the line 3--3 in FIG. 2;

FIG. 4 is an enlargement (5× magnification) of the flexural pivotbearing by which each of the mutually orthogonal mass quadrupole bars issupported in the gradiometer assembly;

FIG. 5A is a still greater enlargement (50× magnification) of thebearing in the region of the web;

FIG. 5B is a view similar to FIG. 5A of an alternative pivot bearing;

FIG. 6 is a more detailed axial cross-section of one of the coil/coilholder assemblies;

FIGS. 7 and 8 are respective end elevations of the assembly shown inFIG. 6; and

FIG. 9 is a schematic of the superconducting circuit for thegradiometer.

BEST MODES FOR CARRYING OUT THE INVENTION

The illustrated apparatus 10 includes a gradiometer assembly 12supported by a biaxial or triaxial gimballed suspension 14 within avacuum can 16. Apparatus 10 forms a dewar probe which may be suspendedinside a dewar (not shown) and immersed therein in liquid helium. Thecan 16 provides an evacuable enclosure which can thereby be maintainedat or near liquid helium temperature for cryogenic operation ofgradiometer assembly 12. A thermal shield 17 may be fitted about thegradiometer assembly to reduce radiative and gas conductive heattransfer between the gradiometer assembly and the vacuum can. The entireequipment including the dewar is readily capable of being mounted in anaircraft or other moving vehicle.

Gradiometer assembly 12 in fact includes two substantially identicalgradiometers, 20, 20' oriented to measure g_(xy) and g_(yx) componentsof the gravitational gradient tensor. The gradiometers 20, 20' arebolted above and below a central box structure 40 and each includes apair of rectangular box enclosures 22, 23 e.g. of niobium, arranged oneinside the other and outer niobium side plates 60 forming a surroundingshield from electromagnetic radiation. Enclosures 22, 23 are typicallyniobium and provide two further levels of all-round electromagneticshielding.

A solid bar 25 of superconducting material such as niobium is mounted ona bearing 21 within the inner enclosure 23 for fine pivotal flexureabout an axis 8 passing substantially through the centre of mass of thebar. The axes of flexure of the two bars 25, 25' are coincident and thebars extend in horizontal planes, mutually orthogonally in the x and ydirections. The provision of a pair of orthogonal bars permits netelimination of common mode rotational accelerations i.e., rotationalnoise at each bar. The gradiometers can, of course, be orienteddifferently depending on the gradient: components of interest.

Each gradiometer 20, 20' further includes an array of superconductingcoils 30 which are mounted on holders 70 in turn supported by the outerenclosure 22. Coils 30 are positioned in close proximity to bar 25.

The dewar (not shown) would typically consist of an outer vacuumcontainer, about 450 mm in diameter and 1.3 a high, and a 300 mmdiameter inner well suspended from the mouth in the top of the outershell by a fibreglass neck tube. The space between the inner well andthe outer shell is permanently evacuated and typically fitted withthermal radiation shields surrounded by numerous layers of aluminisedmylar superinsulation. Vacuum can 16 is supported within the dewar froman aluminium top plate which is attached to the mouth of the dewar. Thetop plate and vacuum can are joined by a neck tube 13 through which thevacuum can is evacuated, for example, down to the range of 10⁻⁸ to 10⁻¹⁰Torr. Gimballed suspension 14 is attached to a rigid 25 mm thickaluminium plate 15 which is bolted to the bottom flange 15a of the necktube and also forms a lid for can 16.

Gimballed suspension 14 consists of three gimbal rings 43, 44, 45mounted on flexural pivots (not detailed) such as Bendix crossed-webpivots. Suspension 14 provides a triaxial rotational isolation forgradiometer assembly 12 and further incorporates respective fibre opticrotation sensors (not shown) for the x and y axes and associatedsuperconducting electromechanical diamagnetic actuators for activestabilisation in a servo circuit controlled by the rotation sensors.

Instead of fibre optic rotation sensors, an optical remote sensingarrangement may be employed, permitting the stabilisation to bephysically separated and enable the utilisation of a room temperaturegyroscope. In this arrangement (not shown), a collimated beam of lightfrom a laser or luminescent diode attached rigidly to a room temperaturegyroscopic inertial reference system is reflected by a plane mirrorattached rigidly to the gradiometer assembly. Rotation of thegradiometer assembly about any axis orthogonal to the light beam canthen be sensed by measurement of the angle between the incident andreflected beams. This is accomplished by means of a position sensitivephoto-detector mounted rigidly to the light source with its planarsensing surface normal to the beam. The detector actually measures the xand y coordinates of the position of the spot of light from thereflected beam and this is used to monitor the relative orientation ofthe gradiometer assembly. Isolation against mechanical vibration, is notillustrated but may be provided in established ways.

Vibrations travelling along the external instrumentation leads to thedewar may be intercepted by the attachment of all cables near theirmid-point to a massive lead block, itself suspended on a soft spring.

Each gradiometer 20, 20' is substantially identical and it is thereforenow proposed to detail only the construction of gradiometer 20, withparticular reference to FIGS. 2 and 3. As already mentioned, enclosures22, 23 are of rectangular box-like configuration each made up of anassembly of top, bottom, side and end plates. Inner enclosure 23 is aclose fit within outer enclosure 22 but arranged to be slid in and outon removal of the bottom plate of outer enclosure 22. The innerenclosure is provided with multiple circular openings 24 whichrespectively receive coil holders 70, and on its bottom. plate 23a, witha bush 26 for the flexure bearing 21 that supports bar 25.

Flexure bearing 21 is detailed in enlarged FIGS. 4 and 5A, 5B and isformed by electric discharge machining (EDM) an almost continuous cut 27through bar 25 parallel to axis 8, save for a microscopically thin web29 extending the width of the bar along axis 8 at the centre of mass ofthe bar. In the example of FIG. 5A cut 27 defines a 270°part-cylindrical core 28 provided with three tapped holes 28a at one endfor attachment of the core to bush 26. The core may of course besupported at both ends, if desired or necessary.

Further tapped holes (not shown) are provided in the bar to containsmall screws whose position can be moved to partly achieve mass balanceof the bar about axis 8. The radial portions 27a of cut 27 are deviatedat their inner ends into right angle segments 27b which are aligned andseparated by web 29. To either side of the web, the cut is bulgedslightly at either side at 27c to lengthen the web and reduce itsstiffness when acting as a pivot. Web 29 defines a micro-pivot some0.030 mm thick, 0.200 mm long and 30 mm "wide", the width of bar 25.FIG. 5B shows an alternative cut to FIG. 5A.

It will be appreciated in particular from FIGS. 4 and 5A, 5B that core28 and the adjacent inwardly projecting land 31 define a pair of memberswith opposed close-spaced regions 28b, 31b or 28b, 31b joined by web 29in a planes extending the width of the bar. These members are adaptedfor pivotal mutual flexure about a pivot axis aligned along web 29. Itwill also be noted that members 28, 31 and the web are comprised of anintegral body of substantially uniform material, in this case niobium.More particularly, the quadrupole bar 25 is capable of fine pivotalflexure on micro-pivot web 29 between angular limits determined bycontact between the opposed faces of the radial portions 27a of cut 27.This angular limit is about 3 degrees and in any event is about theamount which would give rise to inelastic deformation of the web.

The dimensions of bar 25 are selected as 30.00 mm square by 90.0 mmlong, thereby producing a gradient sensor with a natural frequency ofabout 1 Hz in which the sensitivity to accelerations via elasticdeformations of the bar and pivot web 29 are made relatively small.

The mounting of each superconducting coil 30 is best seen in FIGS. 6 to8. Each holder 70, a machined piece of niobium, is of circularcross-section and has an outer peripheral retaining flange 72. Theholder further has a co-axial inner recess 71 for a fibreglass coilformer 74. The coil 30 is a pancake coil, i.e., a flat spiral wound onthe exposed surface of former 74 and held in place by epoxy. The wire80, necessarily superconducting and conveniently niobium with formvarinsulation, enters the centre of the spiral via a diagonal entrance hole76 in former 74, circulates the former several times and exits through achannel in the former. Holes 75 in former 74 are for temporarilyclamping the assembly during winding. Both wire ends pass through a hole78 in holder 70 and then along various channels (not shown) machined inthe outer faces of enclosure 22 and through holes into enclosure 40.

Holders 70 are held in place in registered apertures 24 in theenclosures and are covered by one of the shield plates 60, secured inplace on the outer enclosure 22 by screws 73 or the like. Plates 60, ofwhich there are four on the sides of each enclosure 22, shield the wires80 which run from coils 30 to enclosure 40. The inner end of each coilis substantially co-planar with the inner face of the inner enclosure23, in close proximity to a face of the bar 25.

The coils 30 are disposed with their axes in a common horizontal plane,three along each side and one at each end of the quadrupole bar. Theside coils are arranged in opposed coaxial pairs, one pair with its axisco-planar with axis 8 and the others towards each end of bar 25. The endcoils 30a, 30b on one side are utilised as push coils fordiamagnetically applying a rotational force to, and augmenting thetorsional stiffness of, the superconducting bar in the respectiverotational directions about axis 8. The two opposite coils 30c, 30d onthe other side are utilised for responding by modulation of theirinductance to pivotal flexure of bar 25 arising from a gravitationalgradient across the bar, the respective coils responding to flexure inthe respective rotational directions about axis 8. The remaining fourcoils are also employed as sense coils, but for detecting translationalmovement of the bar in the x and y directions. The coils aresubstantially identical and may therefore be interchangeably employed aseither push coils or sense coils, or both.

The push coils are required to provide feedback damping and to fine-tunethe torsional resonant frequencies of the quadrupole bars to preciselymatch their response to common mode angular accelerations about the axis8.

It will be appreciated that quadrupole bars 25 strictly need not beformed in solid superconducting material such as niobium, so long asthey include superconducting material for interaction with coils 30. Forexample, each bar may be an aluminium mass lined with or treated tocontain niobium at those parts of its surface which face the operationalcoils.

The eight coils of each set are wired in superconducting circuits asschematically depicted in FIG. 9 and detailed remarks concerning thesecircuits are set out hereinafter.

The superconducting wires 80 from the coils are fed through machinedchannels in enclosure 22 to a superconducting joint interface 41 withinenclosure 40. The various required transformers are also housed withinenclosure 40.

Further leads from this interface traverse feedthroughs 46 to theexterior of the assembly. The push coils are operated by employing heatswitches to enable the insertion of controlled persistent currents whilethe means to detect inductance changes in the sense coils comprises oneor more cryogenic SQUIDs (Superconducting Quantum Interference Devices)to sense differential motion. The heat switches and SQUIDs are housedwithin vacuum can 16. The switches and current source are typicallyunder computer control.

As the SQUID sensing system is very sensitive to extremely small changesin magnetic flux, all leads and components are shielded by closedsuperconducting shields, e.g., of fine niobium tubing. External fieldsare exponentially attenuated as they enter the enclosure provided by theshields: the geometry of the tubing is designed so that the earth'sambient magnetic field produces less than one flux quantum inside theshield.

The illustrated apparatus, operated cryogenically, is capable ofmeasuring angular displacements of the order of 10⁻¹² radians. It willbe understood that materials other than niobium may be employed in theconstruction of the illustrated assembly. It is preferred however thatthe materials chosen have similar coefficients of thermal expansion, andthat at least wires, wire shields and bar surfaces are formed insuperconducting material. The enclosures, for good temperature controlare desirably made in a material which is a good conductor of heat tominimise temperature gradients across the gradiometer. The preferredmaterial for the gradiometer body (bars, enclosures, shields) isniobium.

Description of Superconducting Circuits (FIG. 9)

The preferred circuitry for the gradiometer consists of five circuits ofthree different types. These are the MAIN READOUT (FIG. 9A), theACCELERATION MONITOR CIRCUITS (FIG. 9B) and the PUSH CIRCUITS (FIG. 9C).There are two acceleration monitor circuits, for measuring accelerationsin the x and y directions, and two push circuits, for the respectivebars 25, 25'. Before describing the three circuit types some generalnotes are appropriate:

1. The apparatus can, in principle, be oriented to measure any of theoff-diagonal components of the gravity gradient tensor. Throughout thedrawings, the figures all show a gradiometer with the z axis parallel tothe vertical. FIG. 3, which shows the x axis parallel to the long axisof the bar, is the cross section of the lower coil enclosure as shown inFIG. 2. That is, the x axis is parallel with the long axis of the bottombar 25 and the y axis is parallel with that of the top bar 25'.

2. In the circuits, the pancake coils used for sensing a superconductingsurface of a bar are labelled according to their usage. Thus, PUSH 1 andPUSH 2 are push coils, X and Y are acceleration sense coils and θ+ andθ- are rotation sense coils.

3. The circuits consist of several elements. The output of each circuitis from a SQUID whose input is coupled to the rest of its circuit bymeans of a shielded toroidal air-cored transformer. Hence there are fiveSQUIDS, one for each circuit.

4. The inductors are of two types: toroidal or flat spiral (pancake).All the coils which face a bar surface are pancake coils. The remainderof the inductors are toroidal.

5. In the illustrated instrument, a "heat switch" consists of a heaterin close thermal contact with a thin superconducting tube which containsa loop of superconducting wire in good thermal contact with the tube butelectrically insulated from it. The tube provides electromagneticshielding for the loop which is a part of the superconducting circuit.By activating the heater, as part of the loop may be heated to atemperature above its superconducting transition temperature. Thisnon-superconducting part then becomes an electrical resistor which willdissipate any current passing through the loop and will allow theinjection of x new current via the pump leads.

In general, the design of heat switch may be refined or replaced by someother method which allows the dissipation and injection of currents inthe superconducting circuits.

Although in principle, a gravity gradiometer is intrinsicallyinsensitive to linear accelerations, in practice these accelerations mayhave an effect because of limitations in the achievable common modeacceleration rejection ratio and because of second order effects inducedby elastic deformations of the micropivot web 29 and quadrupole bar 25,25'. Consequently, accelerometers are required for the measurement ofaccelerations so that the acceleration effects may be appropriatelysubtracted from the gradient signal and so that the accelerations may berecorded for any subsequent analysis of the data.

The motion of the quadrupole bar 25 or 25' as a result of theaforementioned elastic deformations may be used as an accelerometer, orseparate accelerometers may be mounted on board the gradiometer packageto perform this function. In any case, two accelerometers are used, eachmeasuring the linear accelerations parallel to the long axis of a bar.These are labelled X and Y according to the directions of these axes.The two acceleration monitor circuits (a representative one of which isshown in FIG. 9B), also labelled X and Y, simply perform the function ofproviding acceleration data for recording.

The two push circuits (one for each bar) are identical and only one istherefore shown in FIG. 9C. The following description for one appliesequally to the other.

The push circuit loop carries a persistent current which can be adjustedand stored. The resulting magnetic flux in the loop means that the pushcoils act as magnetic springs thereby increasing the mechanicaltorsional resonant frequency of the bar. This technique is used to matchthe torsional resonant frequencies of the two bars. The rejection ofangular accelerations about the z axis depends on how well thesefrequencies are matched. Modulations of the current will result due toangular motion of the bar and these are sensed by coupling the push loopto a SQUID. This output can be used in feedback to servo control angularaccelerations about the z axis.

The main readout circuit depicted in FIG. 9A performs the function ofcombining the angular information from each of the responders togetherwith the x and y acceleration information to provide a temperaturecompensated output signal proportional to the gravity gradient. Thereare five loops, in each of which the magnetic flux can be independentlyset and then locked. These are: the θ loop for the top bar; the θ loopfor the bottom bar; the X acceleration loop (bottom bar); the Yacceleration loop (top bar); and finally a temperature sensing loop,into which the SQUID input transformer is coupled. Flux in the X,Y loopsis trimmed so that the SQUID output is independent of these twoaccelerations. Similarly the flux in each of the two θ loops is set tocancel the effects of rotational acceleration about the z-axis. Thetemperature loop flux is adjusted to make a first order cancellation ofsmall temperature inhomogeneities in the gradiometer.

We claim:
 1. A gravity gradiometer comprising:a housing; a body locatedwithin the housing; a bearing for mounting the body for rotation aboutan axis passing substantially through the center of mass of the body,said bearing includes a web which undergoes limited elastic deformationin order to permit said rotation of the body about said axis; and aplurality of transducers located within the housing for producing outputsignals in response to rotation of the body about said axis arising froma gravitational gradient across the body.
 2. A gravity gradiometer asclaimed in claim 1, wherein said plurality of transducers are arrangedto apply rotational forces to said body.
 3. A gravity gradiometer asclaimed in claim 2, wherein said rotational forces operate to increasethe effective stiffness of the web.
 4. A gravity gradiometer as claimedin claim 1, 2 or 3, wherein said web is thin but is elongate in thedirection of said axis.
 5. A gravity gradiometer as claimed in claim 4,wherein said bearing comprises a pair of members and said web extendsbetween said members.
 6. A gravity gradiometer as claimed in claim 5,wherein the web is integral with at least one of said members.
 7. Agravity gradiometer as claimed in claim 6, wherein the web is integralwith both of said members.
 8. A gravity gradiometer as claimed in claim6, wherein said members are integral with said body.
 9. A gravitygradiometer as claimed in claim 8, wherein the thickness of the web isless than the length of the net as measured in a direction which isperpendicular to said axis.
 10. A gravity gradiometer as claimed inclaim 9, wherein said web has generally planar opposed parallel facessymmetrically disposed relative to a perpendicular plane which includessaid axis.
 11. A gravity gradiometer as claimed in claim 10, whereinsaid body includes a cut which defines said members and said web andwherein one of the members comprises a core which is coupled to saidhousing and the other of the members comprises an adjacent face of acavity formed in the body by said cut.
 12. A gravity gradiometer asclaimed in claim 11, wherein said core includes a part cylindricalsurface and said cavity includes a portion thereof which iscomplementary thereto.
 13. A gravity gradiometer as claimed in claim 12,wherein the spacing between said cylindrical surface and said portion isuniform.
 14. A gravity gradiometer as claimed in claim 1, wherein saidhousing comprises an electromagnetic shield.
 15. A gravity gradiometeras claimed in claim 14, wherein said transducers comprisesuperconducting coils.
 16. A gravity gradiometer as claimed in claim 14,wherein said body comprises superconducting material.
 17. A gravitygradiometer as claimed in claim 16, wherein said superconductingmaterial is niobium.
 18. An instrument comprising a pair of gravitygradiometers as claimed in claim 1 or 3, the housings of which arecoupled together such that there is no relative movement therebetween.19. An instrument as claimed in claim 18, wherein the axes of thegradiometers are coaxial and the bodies are mutually orthogonal.
 20. Aninstrument as claimed in claim 19, wherein the housings are coupled to agimballed suspension.
 21. An instrument as claimed in claim 20, whereinthe gimballed suspension is biaxial or triaxial.
 22. An instrument asclaimed in claim 21, including a container in which said suspension islocated.
 23. An instrument as claimed in claim 22, including a cryogenicfluid dewar in which said container is located.
 24. A gravitygradiometer as claimed in claim 1, wherein the housing includes a pairof electromagnetic shield enclosures arranged one inside the other andsaid body includes superconducting material and is mounted within theinner of said enclosures and said transducers comprise an array ofsuperconducting coils supported by the outer of said enclosures andpositioned in close proximity to said body.
 25. A gravity gradiometeraccording to claim 24, wherein said two enclosures are close fittingoblong boxes and said body is an oblong solid body of a shapecomplementary to said enclosures.
 26. A gravity gradiometer according toclaim 24, wherein an axis of flexure divides said body into respectivearms of said body to either side of said axis of flexure, and whereinthere is a superconducting coil on opposite sides of each arm.
 27. Agravity gradiometer according to claim 26, wherein there are furthercoils to either side of the body at said axis of flexure and at each endof the body, for monitoring translational movement of said body.
 28. Agravity gradiometer according to claim 24, wherein said superconductingmaterial is niobium.
 29. A gravity gradiometer according to claim 24,supported in a system which is shielded electrically, magnetically,thermally and vibrationally.
 30. A gravity gradiometer according toclaim 24, wherein said bearing is cut from a single mass of asuperconducting material.
 31. An instrument according to claim 26comprising a pair of gravity gradiometers, wherein the housings arecoupled together so that there is no relative movement therebetween andthe axes of flexure of said respective bodies are substantiallyco-incident.
 32. An instrument according to claim 31, wherein the arraysof superconducting coils associated with the two bodies are coupled intofive superconducting loops and, in each loop, magnetic flux can beindependently set and locked, which loops include a first loop includingcoil(s) at one or both ends of one of the bodies, a second loopincluding coil(s) at one or both ends of the other of the bodies, thirdand fourth loops including the coils to apply rotational force to and/orrespond to pivotal flexure of the respective bodies, and a fifth loopresponsive to the temperature about the bodies.
 33. A gravitygradiometer as claimed in claim 5, wherein said pair of members and saidweb are integral with said body.
 34. A gravity gradiometer as claimed inclaim 33, wherein the amount of rotation of said bearing is limited. 35.A gravity gradiometer as claimed in claim 34, wherein the amount ofrotation of said bearing is limited such that said web only undergoeselastic deformation.
 36. A gravity gradiometer as claimed in claim 34,wherein the amount of rotation of said bearing is limited such that thebearing rotates through about 3°.
 37. A gravity gradiometer as claimedin claim 33, wherein the web is about 0.03 mm thick.
 38. A gravitygradiometer as claimed in claim 33, wherein the housing is coupled to agimballed suspension.
 39. A gravity gradiometer as claimed in claim 38,wherein the gimballed suspension is biaxial or triaxial.
 40. A gravitygradiometer as claimed in claim 39, wherein the suspension is mounted ina container which can be immersed in a cryogenic medium.
 41. A gravitygradiometer as claimed in claim 40, wherein said container comprises avacuum can and said medium comprises liquid helium.
 42. A gravitygradiometer as claimed in claim 41, including a dewar for containingsaid liquid helium and said dewar is capable of being mounted in anaircraft or other moving vehicle.